In 1870, German chemist Erich von Wolf analyzed the iron content of green vegetables and accidentally misplaced a decimal point when transcribing data from his notebook. As a result, spinach was reported to contain a tremendous amount of iron—35 milligrams per serving, not 3.5 milligrams (the true measured value). While the error was eventually corrected in 1937, the legend of spinach’s nutritional power had already taken hold, one reason that studio executives chose it as the source of Popeye’s vaunted strength.

The point, according to Samuel Arbesman, an applied mathematician and the author of the delightfully nerdy “The Half-Life of Facts,” is that knowledge—the collection of “accepted facts”—is far less fixed than we assume. In every discipline, facts change in predictable, quantifiable ways, Mr. Arbesman contends, and understanding these changes isn’t just interesting but also useful. For Mr. Arbesman, Wolf’s copying mistake says less about spinach than about the way scientific knowledge propagates.

Copying errors, it turns out, aren’t uncommon and fall into characteristic patterns, such as deletions and duplications—exactly the sorts of mistakes that geneticists have identified in DNA. Using approaches adapted from genetics, paleographers—scientists who study ancient writing—use these accumulated errors to trace the age and origins of a document, much in the same way biologists use the accumulation of genetic mutations to assess how similar two species are to each other. For example, by analyzing the oddities and duplicated errors in the 58 surviving versions of “The Wife of Bath’s Prologue” from Chaucer’s “Canterbury Tales,” researchers deduced the content of the original version.

Mr. Arbesman’s interest in the spread of knowledge also leads him to the story of Brontosaurus, the lovable, distinct herbivore we all grew up with—only it never existed. Originally described in 1879 by Othniel Marsh, the Brontosaurus was soon determined to be a type of dinosaur that Marsh had already discovered in 1877, the Apatosaurus. But since the original Apatosaurus was just “a tiny collection of bones,” while the Brontosaurus that Marsh named “went on to be supplemented with a complete skeleton, beautiful to behold,” the second discovery captured the public’s imagination and the name “Brontosaurus” stuck for nearly a century. Only recently has the name “Apatosaurus” started to gain traction.